selected examples: advantages/inconveniency of powder/single crystal data
DESCRIPTION
Selected examples: advantages/inconveniency of Powder/Single crystal data. A.Daoud-aladine, (ISIS-RAL). Recall: structure factors formulas. For non-polarised neutrons. Nuclear Phase:. Magnetic Phase:. Scattering vector. h=H. Arrangement of the moments. Atomic positions. Structural - PowerPoint PPT PresentationTRANSCRIPT
Selected examples:advantages/inconveniency of Powder/Single crystal data
A.Daoud-aladine, (ISIS-RAL)
0
li l i r R r
1
2 .n
j jj
F b exp i
H H r
nuc ( ) *( )I F F H H H
Nuclear Phase:Scattering
vector h H k
i
k
2li lexp i km S kR
Structure Factor/
Intensity
*h h hM MI
Magnetic Phase:
h=HAtomic positionsStructural
model
Arrangement of the moments
h = ( )- ( ( )) with h h
M M h e e M h e
1
h 2 .n
jj k j
j
p f exp i
M h S h r
*
hh
*
hhhMM NNI
For non-polarised neutrons
Recall: structure factors formulas
Difficulties of single crystal studiesConstant Wavelength (4-circle)TOF-Laue
Powder diffraction and pitfalls of Rietveld refinements
x1
y1
a*
4-circle angles
Sample Reciprocal latticecell and UB matrix
Q=Hx0
y0
kf
ki
1/b*
Punctual or Small area detector
D10
min
max
min
max
D9
Single crystal diffraction: 4-circles
Q=4.sin/
hmi
kfki
x1
y1
a*
Sample Reciprocal latticecell and UB matrix
Q=Hx0
y0
kf
ki
1/b*
1/min
1/max
Goniometer anglesOnly on SXD
SXD
Q=4.sin/
Single crystal diffraction: 4-circles
x1
y1
a*
Sample Reciprocal latticecell and UB matrix
Qx0
y0
kfmax
kfminkf
ki
1/
90° detector
b*
Goniometer anglesOnly on SXD
1/min
1/max
37° detector
SXD
Single crystal diffraction: 4-circles
In a single crystal job, we only need to minimize the difference between the observed and the calculated integrated intensities (G2) or structure factors (F) against the parameter vector I corresponding to magnetic structure parameters only
Observed intensities are corrected for absorption, extinction before the magnetic structure determination
2 2 2, ,( ( ))n obs n calc k I
n k
M w G G
2
1n
n
w
: is the variance of the "observation"2
,obs nG2n
Optimization of extracted integrated intensities
Single crystal diffraction: data treatment
Single crystal diffraction: data treatment
Ex: CaV2O4 (Coll. O.Pieper, B.Lake, HMI)
Extraction of integrated intensities Gobs can de difficult
Motivation: CaV2O4 is a Quasi one dimensional magnet V3+ S=1 => weakly coupled frustrated Haladane chains
TN=75K
J2
J1
J2
J1
Otho-monoclinic
k=( 0 ½ ½ )
Magnetism
Structure
J4
J3
Single crystal diffraction: data treatment
Extraction of integrated intensities Gobs can de difficult
Single crystal diffraction: data treatment
k=( 0 ½ ½ )
(a*,b*) plane(b*,c*) plane
Ex: CaV2O4 (Coll. O.Pieper, B.Lake, HMI)
T=15K T=15K
Extraction of integrated intensities Gobs can de difficult
1st problem: Crystal quality check on SXD
(-4 -2 2), det=11SXD19323.raw
(-9 -8 2), det=10
d=1.35
d=1.22
d=0.71
Orthorhombic Pnam (a=9.20,b=10.77,c=3.01)
=> Monoclinic (~89.6) below T~190K
T=15K
T=15K
Cryst1 (a*,b*) plane
T=15K
(a*,b*) plane
(a*,b*) plane
T=RT
Cryst2
Single crystal diffraction: data treatment
k=( 0 ½ ½ )
(b*,c*) plane
Ex: CaV2O4 (Coll. O.Pieper, B.Lake, HMI)
T=15K
Extraction of integrated intensities Gobs can de difficult
2nd problem: Monoclinic splitting-Crystal Twinning
(a*,b*) plane(-2 k l) planeT=15K
Cryst1
Cryst2
Constant Wavelenght Diffraction : E4-two-axis, (b*,c* plane survey at LT)
12
12
Constant Wavelenght Diffraction : E5-4-circle
(b*,c*)
Data containing
Split peaks
Merged peaks Observations compared to the sumS1.F2(hkl)1 + S2.F2(hkl)2
12
S1.F2(hkl)1 separated from S2.F2(hkl)2
Magnetic structure solution from E5 4-circle (HMI)
Old powder results:
AF F
AF F
F AF
F AF
21
2 1
21
2 1
AF- k=( 0 ½ ½ )
Rf=17%Rf=14%
Canting, but what type?
Rf=14%
Magnetic structure solution
44/2=128constrained models
generated with controlled Canting (2 params each)…
Unconstrained models 3x4=12 params
Rf=6%
Rf=14%
Rf=6%
Rf=6%
Difficulties of single crystal studiesConstant Wavelength (4-circle)TOF-Laue
Powder diffraction and pitfalls of Rietveld refinements
Sample: Crystal
Reciprocal latticePowder averaged
Qkfmax
kfmin
kf
ki
1/1/min
1/max
Powder diffraction
CW-scan ( fixed)
TOF-scan ( fixed)
S
Dkf ki
Ex: DMC-SINQ
Powder diffraction: beneficiate from the power of the rieteveld technique,
d
s2
2
Int
d=Detector opening 90°T=2
Int
. ( )I T T h
. ( )I T T h h h
h
2
Powder diffraction
at the position “i”: Ti
Bragg position Th
yi-yci
( )ci i iy I T T b h hh
The “MODEL”
Intensity yi (obs)
The Rietveld model
List of refinable parameters
2I L APC Fh h
•Ih refinable = profile matching mode •Or Ih modeled by a “structural model”(atom positions, magnetic moments)to calculate the structure factor F2
h h II I
( , )h Pix •Contains the profile, combining instr. resolution, and the additional broadening coming from defects, crystallite size, ...
Bi ib b •Background: noise, diffuse scattering, ...
( )ci i iy I T T b h hh
The “MODEL”
The Rietveld model
Least square refinement of the RM model for powder data
The RM allows refinement of the parameters, by minimising the weighted squared difference between the observed and the calculated pattern against the “parameter vector”: = (I , P , B)
22
1
( )n
i i cii
w y y
21
iiw
2
i : is the variance of the "observation" yi
The Rietveld method
meaning of the result
, ,
,
100obs i calc i
ip
obs ii
y yR
y
R-pattern
1/ 22
, ,
2
,
100i obs i calc i
iwp
i obs ii
w y yR
w y
R-weighted pattern
1/ 2
2,
( )100exp
i obs ii
N P CR
w y
Expected R-weighted pattern
Profile R-factors
, ,
,
' '100
' '
obs k calc kk
B
obs kk
I IR
I
Bragg R-factor
, ,
,
' '100
' '
obs k calc kk
F
obs kk
F FR
F
Crystallographic RF-factor.
,, ,
,
( )( )' '
( )i k obs i i
obs k calc ki calc i i
T T y BI I
y B
,,
' '' ' obs k
obs k
IF
jLp
Crystallographic like R-factors
2
2 wp
exp
R
R
Chi-square N - P +C
The Rietveld method
Powder diffraction: problem of accidental overlap…
Nuclear
Reciprocal space AF order on a centred lattice
b1
b2(110)(-110)
Int
a1
a2
a1
a2
b1
b2(110)
(-100)
(-110)
(010)
(010)
(-100)
(010)
(-100)
(b)(a)(a)
(b)
Nuclear
MagneticMagnetic Absent
Magnetic Absent
Powder diffraction vs. single crystal: main limitations of NPD
• Structure solution methods: simulated annealing (Fullprof)
,, ,
,
( )( )' '
( )i k obs i i
obs k calc ki calc i i
T T y BI I
y B
• Extract (Profile matching)
2 2 2, ,( ( ))n obs n calc k I
n k
M w G G • Minimize
with an algorythm (ex: simulated annealing in Fullprof)
• Constraint the obtained models
• Refine them back the with the Rietveld method
Beyond the Rietveld method
T. Arima, et al.
Phys. Rev. B 66, 140408 (2002)
AF?
Mn3+
+
+
-
-
cmag
YBaMn2O6
DMC(PSI)T=1.5K
• 8 Mn atoms per cell = 24 spin components • No symmetry analysis possible
Powder diffraction : example of quasi-model degeneracy
T. Arima, et al.
Phys. Rev. B 66, 140408 (2002)
New model ??
Powder diffraction : example of quasi-model degeneracy
AF?
Mn3+
+
+
-
-
cmag
DMC(PSI)T=1.5K
Powder diffraction : example of quasi-model degeneracy
Structure determination methods
Except for simple cases, the Rietveld “refinement” can only be a final stage of a magnetic structure determination
Before using it, a maximum number of constraints on the magnetic model are desirable (ex: symmetry analysis), or starting models can be obtained using structure solution approaches
Single crystal data are always better, but can be tricky!
For advanced topics: see the Fullprof Suite documentation and tutorials at:
http://www.ill.fr/dif/Soft/fp/php/tutorials.html